diff --git a/types/jquery/index.d.ts b/types/jquery/index.d.ts
index 0e007b689e..60583af1bc 100644
--- a/types/jquery/index.d.ts
+++ b/types/jquery/index.d.ts
@@ -620,7 +620,7 @@ interface JQuery<TElement extends Node = HTMLElement> {
      * @see {@link https://api.jquery.com/each/}
      * @since 1.0
      */
-    each(fn: (this: TElement, index: number, element: Element) => void | false): this;
+    each(fn: (this: TElement, index: number, element: TElement) => void | false): this;
     /**
      * Remove all child nodes of the set of matched elements from the DOM.
      *
@@ -985,7 +985,7 @@ interface JQuery<TElement extends Node = HTMLElement> {
      * @since 1.0
      * @since 1.4
      */
-    index(element?: Element | JQuery | JQuery.Selector): number;
+    index(element?: JQuery.Selector | Element | JQuery): number;
     /**
      * Set the CSS inner height of each element in the set of matched elements.
      *
diff --git a/types/jquery/jquery-tests.ts b/types/jquery/jquery-tests.ts
index a5b668a9ba..2536144845 100644
--- a/types/jquery/jquery-tests.ts
+++ b/types/jquery/jquery-tests.ts
@@ -3387,6 +3387,82 @@ function JQuery() {
             // $ExpectType JQuery<HTMLElement>
             $('p').slice(0);
         }
+
+        function pushStack() {
+            // $ExpectType JQuery<HTMLElement>
+            $('p').pushStack([new HTMLElement()], 'name', ['arg']);
+
+            // $ExpectType JQuery<HTMLElement>
+            $('p').pushStack([new HTMLElement()]);
+        }
+    }
+
+    function misc() {
+        function serialize() {
+            // $ExpectType string
+            $('p').serialize();
+        }
+
+        function serializeArray() {
+            // $ExpectType NameValuePair[]
+            $('p').serializeArray();
+        }
+
+        function each() {
+            // $ExpectType JQuery<HTMLElement>
+            $('p').each(function(index, element) {
+                // $ExpectType HTMLElement
+                this;
+                // $ExpectType number
+                index;
+                // $ExpectType HTMLElement
+                element;
+            });
+
+            // $ExpectType JQuery<HTMLElement>
+            $('p').each(function(index, element) {
+                // $ExpectType HTMLElement
+                this;
+                // $ExpectType number
+                index;
+                // $ExpectType HTMLElement
+                element;
+
+                return false;
+            });
+        }
+
+        function extend() {
+            // $ExpectType JQuery<HTMLElement>
+            $.fn.extend({ myPlugin: {} });
+        }
+
+        function get() {
+            // $ExpectType HTMLElement
+            $('p').get(0);
+
+            // $ExpectType HTMLElement[]
+            $('p').get();
+        }
+
+        function index() {
+            // $ExpectType number
+            $('p').index('span');
+
+            // $ExpectType number
+            $('p').index(new HTMLElement());
+
+            // $ExpectType number
+            $('p').index($('span'));
+
+            // $ExpectType number
+            $('p').index();
+        }
+
+        function toArray() {
+            // $ExpectType HTMLElement[]
+            $('p').toArray();
+        }
     }
 }